Contest: Large number

This is just for fun. No prizes. I just want to see what people come up with.

The rules are this:
- You need to write in your post a real number (reminder: real numbers are finite by definition).
- The person who writes the largest real number wins
- Your usable characters are limited to 200 characters.
- You need to present your number between CODE brackets so I can count the characters
- Standard mathematical functions are accepted, everything else must be referenced or explained (and the explanation falls within the 200 character limit.
- No references to earlier posts allowed.
- Attempting to replicate (forms of) Berry's paradox is not allowed.

Edit: I see someone has edited the post - note I wasn't sure if the Knuth's notation counts as standard, so I have not used all possible up arrows, leaving place for the "Knuth's notation" name. If if counts as standard, then obviously there should be 198 up arrows.

Yeah, the number of arrows in the second step of 64 steps in calculating Graham's number is larger than the number of Planck volumes in the universe. I've never been so scared of a number.

I actually read an article a while back--can't remember where--by a mathematician who was going to write a satire piece declaring Graham's number to be an upper bound for the integers, effectively making it possible to proof many theorems from number theory by exhaustion.

Then he realized that Graham's number is so big, it really wouldn't make a difference at all when it comes to proofs.

I chose -9.7 in my number because that was the biggest I could get wolfram alpha calculate the value of the expression with, so people could know what it is. Going deeper and deeper into the negative numbers, makes the value of the expression larger and larger. So I can write ##{\LARGE e^{\tan(\frac{\pi}{2}-10^{-10^{100}})}} ##, but...well...who knows what this number is and whether its bigger or smaller than the numbers suggested by others!

I chose -9.7 in my number because that was the biggest I could get wolfram alpha calculate the value of the expression with, so people could know what it is. Going deeper and deeper into the negative numbers, makes the value of the expression larger and larger. So I can write ##{\LARGE e^{\tan(\frac{\pi}{2}-10^{-10^{100}})}} ##, but...well...who knows what this number is and whether its bigger or smaller than the numbers suggested by others!

Definitely smaller. It is very easy using Taylor expansions to compute the number of digits of this number. The numbers posted by others are so large, you'll need special notations to compute the number of digits.

Definitely smaller. It is very easy using Taylor expansions to compute the number of digits of this number. The numbers posted by others are so large, you'll need special notations to compute the number of digits.

Actually you can nest all of these notations together to get bigger and bigger numbers, there is no limit. It seems the restriction to 200 characters is exactly because of this, so people actually should give the biggest number possible that can be represented using 200 characters. But in math you always can invent shorthand notations so even that won't place a limit and I guess this proves that this thread won't terminate.(If it was a computer program...as a thread, it will bore the participants and die out!)
But I like it, Its nice to see people try!

Actually you can nest all of these notations together to get bigger and bigger numbers, there is no limit. It seems the restriction to 200 characters is exactly because of this, so people actually should give the biggest number possible that can be represented using 200 characters. But in math you always can invent shorthand notations so even that won't place a limit and I guess this proves that this thread won't terminate.(If it was a computer program...as a thread, it will bore the participants and die out!)

Nono, since the shorthand notations must be explained within the 200 character limit. This will ensure there definitely is a largest number expressible in 200 characters. After all, there are far less than ##100^{200}## numbers expressible this way. So there definitely is a largest, even though it is hard to find which one it is.

Graham's number uses more arrows than there are Planck volumes in the observable universe for the first step in calculating it. Then it takes the result of that number, and that's the number of arrows for the next step. It repeats that 63 more times, and then you've got Graham's number.

However, with your notation, we could easily say, for instance $$x \uparrow ^{x!} x$$ and it would seem the 200 character limit allows us all the freedom to go arbitrarily large.

By the way, don't try to comprehend the size of that number if ##x## is Graham's number. You might go comatose.

Graham's number uses more arrows than there are Planck volumes in the observable universe for the first step in calculating it. Then it takes the result of that number, and that's the number of arrows for the next step. It repeats that 63 more times, and then you've got Graham's number.

Yeah, that seems to be a large number. But that still doesn't prove its bigger than the number I posted!
Anyway, I can do this: